Recursive and lambda functions
This is a continuation of
exercise 12 b (A function that returns a value)
Recursive functions
We have discussed how to create a function, how to pass an argument to a function and then how to call a function. We have done a lot. It will pay us well if we take breaks frequently.
Kindly take a break to revise what we learnt so far and also take a long break away from PC.
In this exercise, we would discuss more on function. A recursive function calls itself. It does so until the base case becomes false.
Let's implement a factorial function. Our function will take in an integer input. If the input is less than 1, the function returns 1, else we proceed.
Let the integer input be, n. n factorial is, n! = n * (n - 1) * (n - 2) * (n - 3) * ... * 1. Our base case is 1. When we get to 1, we break or terminate the recursive function.
Example 1 - For loop
factorial = 1
n = int(input("Enter n: "))
if n < 1:
print(1)
else:
for i in range(1, n+1):
factorial *= i
print(factorial)
# input output
# 3 6
# 5 720
# 15 1307674368000
Example 2 - Function
Now we shall implement the above using a recursive function.
def factorial(n):
if n < 1:
return 1
else:
return n * factorial(n-1)
-
def factorial(n): we define a function called factorial that take an integer argument,n. -
if n < 1: return 1: we check the base case and return 1. The function returns 1 and the execution stops. -
else: return n * factorial(n-1): ifn > 1, we returnnmultiplied byfactorial(n-1). - If
n=5, we would have that:factorial(5) = 5 * factorial(4)factorial(5) = 5 * 4 * factorial(3)factorial(5) = 5 * 4 * 3 * factorial(2)factorial(5) = 5 * 4 * 3 * 2 * factorial(1)factorial(5) = 5 * 4 * 3 * 2 * 1factorial(5) = 720
Example 3
Implementation of Euclid GCD algorithm. We are interested in the greatest common divisor of two numbers, gcd(a, b).
Algorithm:
- let
a,bbe the two numbers - let
rbe the remainder ofaandb,a % b - check if
ris0,bdividesa, if so, returnb - else assign
btoaandrtoband repeat the second step
a = int(input("Enter a: "))
b = int(input("Enter b: "))
while True:
r = a % b
if r == 0:
print(b)
break
else:
a = b
b = r
# a = 72
# b = 96
# gcd(a, b) = 24
Example 4
Using recursion.
def gcd(a, b):
r = a % b
if r == 0:
return b
else:
return gcd(b, r)
print(gcd(72, 96)) # 24
Let us shorten this code
def gcd(a, b):
if a % b == 0:
return b
return gcd(b, a % b)
Lambda functions
Lambda function is also known as anonymous function - a function without a name. We can say it is a one-time-function. We create a lambda function using the lambda keyword. Simply, (lambda comma-separated-args: body)
Structure
Let's consider a function that increments a given integer by one and returns the value.
def inc(n):
return n + 1
print(inc(2)) # 3
The snippet above uses the def keyword to create the function. Now let's see how we would use the lambda keyword to create the same function.
Example 5
print((lambda x: x+1)(2)) # 3
So the structure of a lambda function is similar to that of normal function. We use the lambda keyword instead of def, the function has no name. Any parameters are space comma-separated from the lambda keyword. The function body is separated by a colon, :.
From example 5, we passed the argument, 2, to the lambda function. Notice how it was passed.
Example 6
We can pass multiple arguments into a lambda function. Note that we can not use return lambda function. Let's use a lambda function to compare two numbers and return the lesser number.
print((lambda a, b: a if a < b else b)(2, 4)) # 2
Normally we would have written,
def min_val(a, b): return a if a < b else b
print(min_val(2, 4)) # 2
This is the same as :
def min_val(a, b):
if a < b:
return a
else: # we can comment out the else:
return b
We can assign a name to a lambda function
Consider example 5 where we increment a given number by one, we can pass the lambda function to a variable and call the variable like a function later.
inc = (lambda n: n + 1)
print(inc(2)) # 3
Can you tell the difference between these two snippets below?
# first func
inc = (lambda x: x + 1)
print(inc(4))
# second func
inc = (lambda x: x + 1)(4)
print(inc)
In the
first func, the lambda function was assigned toinc.incwas called and an argument of value,4was passed. So we can say thatincis a function.In the
second func, an argument of value4was passed to the lambda function. The result was assigned toinc. Soincis just another variable of value,4 + 1 = 5and not a function.
Practicals
- Write a function to sort this list,
[[47, 3, 1, 34], [0. - 3, 4], [7, 21, 13, 37, 8]] - Write a function that returns the temperature from degree Fahrenheit to degree Celsius
- Write a function that returns the sum of numbers between a given range inclusive. If the range is
1 to 5, return15. - Write a function the prints the squares between a given range inclusive
- Write a function that sums up the individual digits in a given integer. Given,
12345, return15 - Write a function that verifies if a given year is a leap year. For a given input to be a leap year, it must be divisible by 4 but(and) not divisible by 100, or the input is divisible by 400.
Summary
- A function is a block of code that performs a specific task
- A function can take at least zero arguments
- function definition
def function_name(some_args):
# some code
- we can call the function by doing
func_name(some_args) - A function allows reuse of code
- A function can be used in any part of our code
- parameters are passed into the function when creating the function
- argument is what we pass to the function when we are calling it
-
returnexits a function and returns a value from the function - use the *arg - tuple argument to collect more arguments
- A function may be called as many times as possible
- A recursive function calls itself
- A lambda function is a nameless function, usually required on the fly
Top comments (1)
Well done